The algebrista

Posted in Language, Mathematics by ths1104 on 17/12/2010

If you like geeky TV shows, I particularly recommend Bones s06ep08 entitled “The Twisted Bones in the Melted Truck”. The title alone should convince the best of you who know that it is impossible to twist bones because bones don’t melt ! But these guys are the specialists, so they will really find twisted bones and even provide a scientific explanation to that [1]. What’s even stronger is that they untwist them just for your pleasure. Check this out !

ALL THE RIGHTS OF THE CLIPS BELONG TO THE CHANNEL FOX. This video is used for comment purpose of Bones season 6 episode 8 where it is stated that Gerolamo Cardano wrote a set of mathematical equations to describe the skeleton system. Believing that comment and critique are at the very core of the fair use doctrine as a safeguard for freedom of expression, we claim it is a fair use under copyright law.

I should confess that I wasn’t familiar with Gerolamo Cardano prior to this.  Cardano is a famous algebraist known for his publication of the solutions to the cubic and quartic equations. And as there is no general algebraic solution to polynomial equations of degree five or higher [2], Cardano couldn’t do more. Besides he was the first to publish the use of complex numbers in calculations even if he did not understand their properties. Among his many other contributions, he invented the Cardan shaft with universal joints and published the horoscope of Jesus… Concerning the set of mathematical equations written by Cardano to describe the skeleton system mentioned in this episode of Bones, I found no reference of their existence.

If Cardano didn’t publish such equations, why did the scriptwriters made reference to him there ? They have obviously done some research, but maybe it’s a confusion due to the fact that in Biomechanics, angles named “cardan angles” can be used to describe the kinematic of the limbs [3]. Another plausible explanation can be found looking for the etymology of the word “algebra”. It comes from Arabic al-jebr  and refers to the setting or the straightening out of broken bones, to the “reduction” of a fracture. In Spanish “algebrista”  still designs a bonesetter. In Mathematics, the word has been introduced in 820 by al-Khwārizmī to describe the operations of  “reduction” and balancing, i.e. the cancellation of like terms on opposite sides of the equation [4]. Nowadays one still talks of “reducing” fractions to lowest terms. Knowing this, Cardano’s 1545 book title Artis Magnæ, Sive de Regulis Algebraicis could be translated by About The Great Art, or The Rules of  Bone Setting… (Mmmmh…) A bit too subtle maybe?


  1. See K. Killgrove comments about that.
  2. Abel’s impossibility theorem
  3. S. J. Tupling and M. R. Pierrynowski, “Use of cardan angles to locate rigid bodies in three-dimensional space”, Medical and Biological Engineering and Computing, Vol. 25, Nb. 5, pp. 527-532, 1987.
  4. C. B. Boyer and U. C. Merzbach, “A History of Mathematics”, second edition, John Wiley & Sons, 1991, ISBN0471543977.

And without the Rosetta Stone ? part.2

Posted in Language by ths1104 on 21/11/2010

See: And without the Rosetta Stone ? part.1

The first thing to be done when trying to translate such a text seems to transliterate it. It will then be easier to analyse it with common data mining tools. The text being written in Greek alphabet, we can use tools such as to obtain the transliteration of our text:

euthys de parastas moi Peisandros “andres” ephē “bouleutai, egō ton andra touton endeiknyō hymin siton te eis tous polemious eisagagonta kai kōpeas.” kai to pragma ēdē pan diēgeito hōs epeprakto. en de tō tote ta enantia phronountes dēloi ēsan ēdē hoi epi stratias ontes tois tetrakosiois. kagō — thorybos gar dē toioutos egigneto tōn bouleutōn — [kai] epeidē egignōskon apoloumenos, euthys prospēdō pros tēn hestian kai lambanomai tōn hierōn. hoper moi kai pleistou axion egeneto en tō tote: eis gar tous theous echonta oneidē houtoi me mallon tōn anthrōpōn eoikasi kateleēsai, boulēthentōn te autōn apokteinai me houtoi ēsan hoi diasōsantes. desma te hysteron kai kaka hosa te kai hoia tō sōmati ēneschomēn, makron an eiē moi legein. hou dē kai malist᾽ emauton apōlophyramēn: hostis touto men en hō edokei ho dēmos kakousthai, egō anti toutou kaka eichon, touto de epeidē ephaineto hyp᾽ emou peponthōs, palin au kai dia tout᾽ egō apōllymēn. hōste hodon te kai poron mēdamē eti einai moi eutharsein: hopoi gar trapoimēn, pantothen kakon ti moi ephaineto hetoimazomenon. all᾽ homōs kai ek toutōn toioutōn ontōn apallageis ouk estin ho ti heteron ergon peri pleionos epoioumēn ē tēn polin tautēn agathon ti ergasasthai.

Of course for an unknown script, a transliteration table has to be created.

The next step would probably be to compile some statistics. What could be interesting to know ? What program should I use ?

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And without the Rosetta Stone ? part.1

Posted in Language by ths1104 on 13/11/2010

Is it possible to translate a text written in an unknown language ?

Suppose Greek is an unknown language. You have found an old document with the following script. You want to translate it. What would you do ?

εὐθὺς δὲ παραστάς μοι Πείσανδρος “ἄνδρες” ἔφη “βουλευταί, ἐγὼ τὸν ἄνδρα τοῦτον ἐνδεικνύω ὑμῖν σῖτόν τε εἰς τοὺς πολεμίους εἰσαγαγόντα καὶ κωπέας.” καὶ τὸ πρᾶγμα ἤδη πᾶν διηγεῖτο ὡς ἐπέπρακτο. ἐν δὲ τῶ τότε τὰ ἐναντία φρονοῦντες δῆλοι ἦσαν ἤδη οἱ ἐπὶ στρατιᾶς ὄντες τοῖς τετρακοσίοις. κἀγώ — θόρυβος γὰρ δὴ τοιοῦτος ἐγίγνετο τῶν βουλευτῶν — [καὶ] ἐπειδὴ ἐγίγνωσκον ἀπολούμενος, εὐθὺς προσπηδῶ πρὸς τὴν ἑστίαν καὶ λαμβάνομαι τῶν ἱερῶν. ὅπερ μοι καὶ πλείστου ἄξιον ἐγένετο ἐν τῷ τότε: εἰς γὰρ τοὺς θεοὺς ἔχοντα ὀνείδη οὗτοί με μᾶλλον τῶν ἀνθρώπων ἐοίκασι κατελεῆσαι, βουληθέντων τε αὐτῶν ἀποκτεῖναί με οὗτοι ἦσαν οἱ διασῴσαντες. δεσμά τε ὕστερον καὶ κακὰ ὅσα τε καὶ οἷα τῷ σώματι ἠνεσχόμην, μακρὸν ἂν εἴη μοι λέγειν. οὗ δὴ καὶ μάλιστ᾽ ἐμαυτὸν ἀπωλοφυράμην: ὅστις τοῦτο μὲν ἐν ᾧ ἐδόκει ὁ δῆμος κακοῦσθαι, ἐγὼ ἀντὶ τούτου κακὰ εἶχον, τοῦτο δὲ ἐπειδὴ ἐφαίνετο <εὖ> ὑπ᾽ ἐμοῦ πεπονθώς, πάλιν αὖ καὶ διὰ τοῦτ᾽ ἐγὼ ἀπωλλύμην. ὥστε ὁδόν τε καὶ πόρον μηδαμῇ ἔτι εἶναί μοι εὐθαρσεῖν: ὅποι γὰρ τραποίμην, πάντοθεν κακόν τί μοι ἐφαίνετο ἑτοιμαζόμενον. ἀλλ᾽ ὅμως καὶ ἐκ τούτων τοιούτων ὄντων ἀπαλλαγεὶς οὐκ ἔστιν ὅ τι ἕτερον ἔργον περὶ πλείονος ἐποιούμην ἢ τὴν πόλιν ταύτην ἀγαθόν τι ἐργάσασθαι.

Some precisions :

  • No Greek dictionary, no Rosetta Stone…
  • Suppose this is the unique document available.
  • As the problem to know whether a script is written with phonetic characters or not is already in itself a difficult issue, to simplify things you can suppose to begin that the text you try to translate is actually written with an alphabet. And that’s why I choose a text in Greek.
  • I choose this text randomly among the collection of texts of the Perseus Digital Library.  A translation is available but please don’t use it. Don’t cheat with Google translate 😉
  • All suggestions are welcome. If you have any idea, whether you have the time to explore it or not, please post it here before.

Edit (Nov 21st, 2010)

It can be argued that even if Greek is an unknown language, some European languages are descended from it. We should then find some graphic analogy between Greek and modern languages. I would probably allow us to translate some words from the original text. But I am not interested in this kind of considerations here because I am searching a general method to translate any unknown language. So let’s say this text has no relation with any known language.

This paragraph is just to remember that I am aware that Greek is inherently close to English, as sentence for example have the same structure in both languages. It will therefore facilitate our analysis. But if the analysis is successful we will try to translate other languages.

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